The universal probabilistic nature of quantum mechanics leads us to work regularly with probabilities. Moreover, if we investigate areas related to experiments or physical realizations, this probabilistic nature of quantum mechanics becomes even more visible. Furthermore, some exotic features such as entanglement arise from quantum mechanics, which are directly related to the probabilistic properties of the quantum system. In the quantum estimation framework, the background of the parameter estimation problem remains virtually unchanged from the classical framework. Here, an unknown parameter \(\theta \)  encoded in a quantum state \(\rho _{\theta }\)  builds a quantum statistical model, then individual qubits can be measured using POVM measurements and these results \(\left\lbrace \theta _{1},...,\theta _{n}\right\rbrace \)  are used for the construction of an estimate \( \theta \) . The major distinction from the classical case is that the probability density function \(p\left(x; \theta \right)\)  is not arbitrary, but is a function that depends on both the quantum state \(\rho \)  and the applied measurement. Moreover, the results of the POVM measurements \(\left\lbrace \theta _{1},...,\theta _{n}\right\rbrace \) , analogous to \(\left\lbrace x_{1},...,x_{n}\right\rbrace \)  in the classical framework, are not necessarily independent of each other due to the quantum correlations existing in the probe quantum state. This allows estimates to be made with a super-classical precision known as the Heisenberg limit [1]}, [2]}.
